Abstract
Investigating scale-free (i.e., fractal) functional connectivity in the brain has recently attracted increasing attention. Although numerous methods have been developed to assess the fractal nature of functional coupling, these typically ignore that neurophysiological signals are assemblies of broadband, arrhythmic activities as well as oscillatory activities at characteristic frequencies such as the alpha waves. While contribution of such rhythmic components may bias estimates of fractal connectivity, they are also likely to represent neural activity and coupling emerging from distinct mechanisms. Irregular-resampling auto-spectral analysis (IRASA) was recently introduced as a tool to separate fractal and oscillatory components in the power spectrum of neurophysiological signals by statistically summarizing the power spectra obtained when resampling the original signal by several non-integer factors. Here we introduce multiple-resampling cross-spectral analysis (MRCSA) as an extension of IRASA from the univariate to the bivariate case, namely, to separate the fractal component of the cross-spectrum between two simultaneously recorded neural signals by applying the same principle. MRCSA does not only provide a theoretically unbiased estimate of the fractal cross-spectrum (and thus its spectral exponent) but also allows for computing the proportion of scale-free coupling between brain regions. As a demonstration, we apply MRCSA to human electroencephalographic recordings obtained in a word generation paradigm. We show that the cross-spectral exponent as well as the proportion of fractal coupling increases almost uniformly over the cortex during the rest-task transition, likely reflecting neural desynchronization. Our results indicate that MRCSA can be a valuable tool for scale-free connectivity studies in characterizing various cognitive states, while it also can be generalized to other applications outside the field of neuroscience.
Highlights
Many dynamical systems ranging from functional brain networks (Achard et al, 2008; Ciuciu et al, 2014) through geophysical systems (Campillo and Paul, 2003; Marinho et al, 2013), natural phenomena (Mandelbrot, 1983) or meteorological data (Vassoler and Zebende, 2012) to financial markets (Podobnik and Stanley, 2008; He and Chen, 2011) have been shown to express scalefree correlations both in the univariate dynamics of their individual constituents, as well as in their interactions
For a better assessment and understanding of fractal connectivity, methods are called for that can eliminate the effects of such scale-dependent interactions and separate the scale-free component of statistical interdependence. This is the primary focus of this paper; here, we propose an extension of Irregular-resampling auto-spectral analysis (IRASA) to the bivariate case, which we title multiple-resampling crossspectral analysis (MRCSA) for isolating the fractal component of the cross-spectral density of a pair of neurophysiological signals
It can be concluded that multiple-resampling cross-spectral analysis (MRCSA) is robust against the presence of multiple oscillatory peaks, as well as it is largely unaffected by the amplitude of oscillatory components
Summary
Many dynamical systems ranging from functional brain networks (Achard et al, 2008; Ciuciu et al, 2014) through geophysical systems (Campillo and Paul, 2003; Marinho et al, 2013), natural phenomena (Mandelbrot, 1983) or meteorological data (Vassoler and Zebende, 2012) to financial markets (Podobnik and Stanley, 2008; He and Chen, 2011) have been shown to express scalefree (or fractal) correlations both in the univariate dynamics of their individual constituents, as well as in their interactions. The power-law relationship is commonly characterized in the obtained fractal scaling exponent, which is referred to as the Hurst exponent (H) or the spectral slope (β) in the time and frequency domains, respectively, with an explicit equivalence between the two (Eke et al, 2000; Kristoufek, 2014) Given that identifying such long-term couplings between various brain regions can reveal novel implications on the functional organization of the brain – that cannot be identified otherwise via single-scale or scale dependent analyses –, fractal connectivity studies gained growing interest recently (Achard et al, 2008; Ciuciu et al, 2014; Stylianou et al, 2020, 2021; La Rocca et al, 2021)
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